Speaker: Jung Hwan Kim KRS presentation (May 27. 2016) Including Below Detection Limit Samples in Decommissioning Soil Sample Analyses Speaker: Jung Hwan Kim KRS presentation (May 27. 2016)

Contents Introduction Purpose of the research Case study Results Conclusions Future work References

Introduction

Introduction Decommissioning is an emerging international issue in the nuclear industry. Termination of an NPP license, involves releasing the facility from regulatory control for either restricted or unrestricted use in the future. Current Domestic Research Focuses on; Development of Clearance Standards Evaluation of Exposure.

Introduction NPP site soil analysis for license termination There are technical problems for finalizing regulations and standards. Hot Spots Observations reported as below the detection limits Observations reported as below the detection limits are caused by: Inherent limitations of measurement methods (e.g. detectors)

Introduction Conventional methods for analyzing soil sampling data: Only use values above detection limit (This ignores non-detects) Replace non-detects with zero Replace non-detects with half of the detection limit (DL) Replace non-detects with DL However, these strategies have limitations: Statistically biased estimate Probabilistic Exposure Assessment is unreliable Predicts a higher dose --- causing higher waste volumes and associated costs

Introduction To resolve these issues Statistical Techniques were used to analyze a case study Proposed methods for estimating summary statistics (Mean, STD DEV, PCT) Kaplan-Meier Regression on Order Statistics (ROS) Maximum Likelihood Estimation (MLE) Proposed method for estimating confidence intervals Bootstrapping These techniques are used by many researchers in the Environmental Science and Technology area.

Introduction – Kaplan-Meier The Kaplan-Meier method is a nonparametric technique which is the most commonly used for calculating the probability distribution to estimate summary statistics with censored data. Kaplan-Meier is nonparametric, so it does not assume the data follow a known distribution. Kaplan-Meier is well-suited for many environmental data sets because it is nonparametric.

Introduction – Kaplan-Meier Consider the following data set: 20, 20, 10, 1, <0.5, <0.5, <25, <2, <2, 1, 100, 30, 3, <3, 2, 1, 3, 5, <10, <0.5 Order this data set in decreasing order (Efron’s bias correction): 100, 30, <25, 20, 20, 10, <10, 5, 3, 3, <3, 2, <2, <2, 1, 1, 1, <0.5, <0.5, 0.5 The probability of each data point is as below: The probability of getting a data point less than 100 is 19/20=0.95 The probability of getting a data point below 30 is 18/19=0.947 The location of 30 on the PDF is calculated by 0.95*0.947=0.90 The probability of getting a data point below 20 is 15/17=0.882 The location of 20 on the PDF is calculated by 0.90*0.882=0.794

Introduction – Kaplan-Meier Value Probability 100 0.95 30 0.90 20 0.794 10 0.741 5 0.684 3 0.570 2 0.507 1 0.253 0.5 Table 1. Kaplan-Meier example data Fig. 1. Kaplan-Meier method example data plot

Introduction – ROS Robust regression on order statistics (ROS) is a semi-parametric method that can be used to estimate summary statistics with censored data. ROS plots the detected values on a probability plot and calculates a linear regression line in order to estimate the parameters. ROS internally assumes that the underlying population is normal or lognormal. However, the assumption is applied to only the censored data set and not to the full data set. It is necessary to fit a known distributional model to the detected values on a probability plot.

Estimated Concentration Introduction – ROS Input Concentration Probability Estimated Concentration 3.2 0.972 2.8 0.944 <2 0.815 1.418 0.713 1.143 0.611 0.954 0.509 0.807 0.407 0.683 0.306 0.572 0.204 0.465 0.102 0.349 1.7 0.873 1.5 0.829 Table 2. ROS final data

Introduction – MLE Maximum likelihood estimation (MLE) is a parametric, model-based method that can be used to estimate summary statistics with censored data. Probability plots and other goodness-of-fit techniques should be used to find matching distributions. Nondetects are distributed in a manner similar to the detected values. If the assumed model is incorrect, MLE may lead to misleading results.

Introduction – Bootstrap After generating 100 bootstrap samples, it is possible to find the confidence interval for the mean, calculating the difference between the mean of the original sample and the mean of bootstrap samples. Bootstrap1 Bootstrap100 Original sample Fig. 2. Schematic matrix of original smaple and bootstrap samples

Purpose of the research “Develop a statistical approach that more accurately estimates the required site decontamination necessary to meet current cleanup criteria and validate that compliance.” The expected advantages are: Better Probabilistic Exposure Assessment More Cost Effective

Case study

Case study There is a monazite powder manufacturing plant. Some of the plant facilities and soil were contaminated during the manufacturing process. Facility soil was decontaminated and soil survey conducted.

Case study The survey consisted of Grid box No.1 and Grid box No.2, each having 30 data points measuring the concentration of U-238 and K-40, in the same area. In Grid box No.1, 8 data points are below the detection limit for U-238, and 17 for K-40. Grid box No.1 U-238 K-40 (8/30) (17/30) Fig. 3. Schematic diagram of Grid box No.1

Case study In Grid box No.2, 10 data points are below the detection limit for U-238, and 9 for K-40. Grid box No.2 U-238 K-40 (10/30) (9/30) Fig. 4. Schematic diagram of Grid box No.2

Results

U-238 in Grid box No.1 Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring   Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring 0.339 0.212 0.123 0.351 0.534 Zero 0.249 0.236 0.012 0.148 0.460 1/2 DL 0.261 0.223 0.048 DL 0.274 0.211 0.095 MLE(ln) 0.263 0.221 0.065 0.486 ROS(ln) 0.267 0.218 0.085 K-M 0.051 Table 3. Summary statistics using several estimation methods – U-238 in Grid box No.1

K-40 in Grid box No.1 Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring   Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring 0.092 0.042 0.072 0.094 0.110 Zero 0.040 0.054 0.087 1/2 DL 0.043 0.051 0.006 DL 0.046 0.049 0.012 MLE(ln) 0.003 0.091 ROS(ln) K-M 0.044 Table 4. Summary statistics using several estimation methods – K-40 in Grid box No.1

U-238 in Grid box No.2 Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring   Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring 0.492 0.274 0.228 0.408 0.7735 Zero 0.328 0.324 0.242 0.561 1/2 DL 0.346 0.305 0.055 DL 0.364 0.288 0.109 MLE(ln) 0.353 0.299 0.102 0.604 ROS(ln) 0.358 0.294 K-M 0.379 0.277 0.213 0.583 Table 5. Summary statistics using several estimation methods – U-238 in Grid box No.2

K-40 in Grid box No.2 Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring   Mean (Bq/g) STD DEV Pct25 Median Pct75 Ignoring 0.092 0.067 0.023 0.108 0.135 Zero 0.064 0.070 0.026 0.124 1/2 DL 0.066 0.069 0.006 DL 0.068 0.013 MLE(ln) 0.011 0.128 ROS(ln) 0.012 K-M 0.127 Table 6. Summary statistics using several estimation methods – K-40 in Grid box No.2

Confidence interval using MLE/Bootstrap Cases 90% confidence interval for the mean (Bq/g) 95% confidence interval U-238 in Grid box No.1   (Mean : 0.263) [0.189, 0.413] [0.177, 0.450] K-40 in Grid box No.1 (Mean : 0.043) [0.025, 0.176] [0.022,0.233] U-238 in Grid box No.2 (Mean : 0.353) [0.256, 0.554] [0.240, 0.604] K-40 in Grid box No.2 (Mean : 0.067) [0.043, 0.142] [0.039, 0.165] Table 7. Various confidence intervals for the mean using MLE/Bootstrap

Background - RESRAD RESRAD is a computer model designed to estimate radiation doses and risks from RESidual RADioactive materials. RESRAD code is used for determining regulatory compliance. Both the U.S Department of Energy and the U.S. Nuclear Regulatory Commission use 25 mrem/yr as the general limit or constraint for soil cleanup or site decontamination. RESRAD code has the basic models and parameters, but it can be modified to meet specific need.

Background - RESRAD RESRAD code can be used to : Compute potential annual doses or lifetime risks to workers or members of the public resulting from exposures to residual radioactive material in soil Support an ALARA analysis or a cost benefit analyses that can help in the cleanup decision-making process. Fig. 5. Exposure pathways considered in RESRAD

Background - RESRAD Assumptions Farmer scenario (Consider all pathways) Municipal landfill Climate data in Daejeon National nutrition survey Default value Did not consider radon and C-14

Results Cases Maximum Total Dose (t) (mrem/yr) Maximum Excess Cancer Risk (t) Ignoring 29.11 (t=128.3yr) 1.127E-3 (t=100yr) Zero 13.09 (t=128.4yr) 4.985E-4 (t=100yr) 1/2 DL 14.15 (t=128.4yr) 5.396E-4 (t=100yr) DL 15.99 (t=128.3yr) 6.114E-4 (t=100yr) MLE 14.13 (t=128.4yr) 5.388E-4 (t=100yr) Table 8 Maximum Total Dose (t) and Maximum Excess Cancer Risk (t) for the several estimation methods in Grid box No.1

Conclusions Summary statistics and confidence intervals were compared to conventional methods. Proposed methods (MLE, ROS, K-M) were performed using the soil samples from the monazite powder manufacturing plant. The preliminary evaluation shows that the proposed method can be effectively used to provide Best Estimate Radioactivity levels at decommissioned NPP site. Estimates of uncertainty in the Mean Values RESRAD is used to estimate radiation doses and risks in each case. Cover thickness is calculated to show the difference between the each method.

Future work Get the soil data from real decommissioned NPP and conduct all of the above analyses (Yankee Rowe Finished/software & codes). Economic analysis of the degree of savings using new methodology. Develop RESRAD input code that allows the inclusion of non-detects.

References [1] Dennis R. Helsel (2005), Nondetects And Data Analysis: Statistics for censored environmental data, John Wiley & Sons, Inc., Hoboken, New Jersey. [2] Zhao, Y., and H.C. Frey, “Quantification of Uncertainty and Variability for Air Toxic Emission Factor Data Sets Containing Non-Detects,” Annual Meeting of the Air & Waste Management Association, Pittsburgh, PA, June 2003 [3] OECD NEA, Cost Estimation for decommissioning: An International Overview of Cost Elements, Estimation Practices and Reporting Requirements, p. 7, 2010 [4] Orbitech, Development of Radioactivity Inference Method and Acceptance Criteria Based on Statistical Approach for Treatment or Disposal of NORM Waste, Feb 2016 [5] Brookhaven National Laboratory, Assessment of Radionuclide Release from Contaminated Concrete at the Yankee Nuclear Power Station, March 2004 [6] Argonne National Laboratory, Examination of Technetium-99 Dose Assessment Modeling with RESRAD (onsite) and RESRAD-OFFSITE, June 2011 [7] EPA, Data Quality Assessment: Statistical Methods for Practitioners, Feb 2006 [8] KHNP, Decontamination Experiment of Contaminated Soil and its Safety Assessment by Residual Radioactivity, 2004 [9] KINS, Establishment of Management Plan for the Disposal of NORM Wastes and Unsuitable Processed Products, Feb 2015

Thank you

Appendix

Background Instruments & Analysis Program ORTEC HPGe (GEM-60195-P, 60% efficiency) is utilized. Counting time is 1,800 sec for all the samples. ORTEC GammaVision 6.01 is used to analyze.

Amount of available data Appendix Amount of available data Percent Censored < 50 observations > 50 observations < 50% nondetects Kaplan-Meier 50 – 80% nondetects MLE or ROS MLE > 80% nondetects Report only % above a meaningful threshold May report high sample percentiles (90th, 95th) Table 8. Recommended methods for estimation of summary statistics

Appendix – Kaplan-Meier The nonparametric Kaplan-Meier (K-M) method has always been considered as a standard method for estimating summary statistics of censored survival data. Left-censored data must be flipped prior to using the K-M method, the procedures of calculating survival probability are computed in a way that is similar to analyses for right censored data, and the results are re-transformed when calculating estimates(mean, median, and other percentiles). In this case, the highest observed value would have the lowest rank 1. Let S be the survival probability. The survival probability is a product of incremental probabilities that are the probabilities of "surviving" to the next lowest detected limit, given the number of data at and below that detection limit. The mean of K-M estimator is evaluated as the area under the K-M survival curve for the flipped data after re-transformation.

Appendix – ROS ROS calculates summary statistics with a regression equation on a probability plot, and is called "regression on order statistics". We used a robust approach to ROS. Unobserved values are estimated from a regression equation obtained by using observed data. The regression equation is obtained by fitting observed values to the probability plot, and the explanatory variable in the regression is the normal scores of observed values.

Appendix – MLE The parametric Maximum Likelihood Estimator (MLE) assumes a distribution that will closely fit the observed data.

Appendix – MDA Calculation 𝑀𝐷𝐶𝑅= 𝑘 2 𝑇 𝑠 +2𝑘 𝐶 𝑏 𝑇 𝑠 + 𝐶 𝑏 𝑇 𝑏 𝑘 : standard score 𝑇 𝑠 : Sample Counting Time 𝑇 𝑏 : Background Counting Time 𝐶 𝑏 : Background Count Rate 𝑀𝐷𝐴= 𝑀𝐷𝐶𝑅 ×𝐹 𝐸 𝑓𝑓 ×𝑉(𝐿) 𝐹 : 4.50×10 −1 pCi/dpm 𝐸 𝑓𝑓 : Counting efficiency 𝑉(𝐿) : Volume of Sample

Results Cases Cover thickness Ignoring -> MLE (29.11->14.13 mrem/yr) More than 3m DL -> MLE (15.99->14.13 mrem/yr) 1/2 DL -> MLE (14.15->14.13 mrem/yr) 13.5cm Table 7. Cover thickness calculated to show the difference between the each method

Introduction – ROS Calculating the plotting position: 𝑝𝑒 𝑖 = 𝑝𝑒 𝑗+1 + 𝐴 𝑗 𝐴 𝑗 + 𝐵 𝑗 [1− 𝑝𝑒 𝑗+1 ] 𝐴 𝑗 = the number of observations detected between the jth and (j+1)th detection limits 𝐵 𝑗 = the number of observations, censored and uncensored below the jth detection limit The number of nondetects below the jth detection limit is defined as 𝐶 𝑗 : 𝐶 𝑗 = 𝐵 𝑗 − 𝐵 𝑗−1 − 𝐴 𝑗−1 Calculating the plotting position: For observed values 𝑝𝑑 𝑖 =(1− 𝑝𝑒 𝑗 )+ 𝑖 𝐴 𝑗 +1 [ 𝑝𝑒 𝑗 − 𝑝𝑒 𝑗+1 ] For censored observations 𝑝𝑐 𝑖 = 𝑖 𝐶 𝑗 +1 ∗[1− 𝑝𝑒 𝑗 ]

Case study The survey consisted of Grid box No.1 and Grid box No.2, each having 30 data points measuring the concentration of U-238 and K-40, in the same area. In Grid box No.1, 8 data points are below the detection limit for U-238, and 17 for K-40. U-238 K-40 MDA Minimum (Bq/g) 0.00997 0.00369 Maximum 0.0953 0.0118 Grid box No.1 U-238 K-40 (8/30) (17/30) Fig. 3. Schematic diagram of Grid box No.1 Table 3. MDA of U-238 and K-40 in Grid box No.1

Case study In Grid box No.2, 10 data points are below the detection limit for U-238, and 9 for K-40. U-238 K-40 MDA Minimum (Bq/g) 0.0111 0.00339 Maximum 0.109 0.0126 Grid box No.2 U-238 K-40 (10/30) (9/30) Fig. 4. Schematic diagram of Grid box No.2 Table 4. MDA of U-238 and K-40 in Grid box No.2